All Questions

Filter by
Sorted by
Tagged with
0
votes
0answers
3 views

What is congruence in lambda-calculus

I see a lot of lecture notes where the terms "congruence" (ex: congruence relation) or deriving usages such as "the expression e is alpha-congruent to e2". Could someone please ...
0
votes
0answers
10 views

Different definitions of grammar complexity

It's known that there are different "kinds" of grammar complexity of language $L$ --- nonterminal complexity (minimal possible $|N|$ for grammar $(N, \Sigma, P, S)$ generating $L$), covering ...
0
votes
0answers
7 views

Optimum partitioning of vertices into mutually disjoint subsets in a weighted graph

tl;dr I'm trying to partition my students into groups with respect to their preferences, i.e. they can declare if they want to be with someone in a group or if they do not want to be with someone in a ...
0
votes
0answers
32 views

Are maximum independent set and minimum clique cover also cover-packing problems?

Maximum independent set and minimum edge cover are a pair of related problems and are cover-packing problems. (Also see p114 of West's Introduction to Graph Theory) Are maximum independent set and ...
0
votes
0answers
17 views

Are Graph Databases computationally equivalent to relational algebra

I am wondering if it can be shown that graph databases along with the graph database model and cypher queries are computationally equivalent to relational algebra. More specifically can cypher queries ...
-3
votes
0answers
9 views

Help find algorithm for array-based task

Given array if numbers a[1..n]. Pair of numbers (i, j) is interesting, if i < j и a[i] > 2a[j]. How to count number of interesting pairs in O(nlogn)? What is the solution? My solution is not ...
6
votes
2answers
100 views

Why should we believe that $NEXP \not \subset P/poly$

I am sorry if this is not an advanced question. Most computer scientists believed that $Nexp \not \subset P/poly$ but they are not even close to this assumption. The main evidence that they are used ...
2
votes
1answer
42 views

Tableau method for two-variable first-order logic

$FO^2$, i.e. two-variable first-order logic, has a NEXPTIME-complete satisfiability problem (see Grädel, Kolaitis and Vardi '97). However, the decidability and complexity of this fragment is proved by ...
0
votes
0answers
20 views

A variant of randomized co-ordinate descent

Let us consider the following optimization problem. $\mathcal{P} =\{P_1,\cdots,P_n\}$, where $P_i\subset\mathbb{R}^d$. Let $m = max_i\lvert P_i\rvert$. The goal is to find a point $c$ such that ...
-3
votes
0answers
57 views

Complexity implications of impossibility of direct Diffie-Hellman compromise

Given generator $g$ of a multiplicative group mod a prime $p$ the Diffie Hellman problem is to find $$g^{xy}\bmod p$$ from $g^x\bmod p$ and $g^y\bmod p$. The best way to solve this is through discrete ...
1
vote
0answers
46 views

Hardness of Approximation of Continuous Metric k-Median

First let me describe the metric $k$-median problem. Definition (Metric $k$-Median): Given a set $C$ of clients and a set $L$ of facility locations defined over a distance metric $d$. Open a set $F$ ...
-2
votes
0answers
57 views

How could we implemented orthogonality with Miranda, Haskell, Julia, Scheme, and Erlang languages? [closed]

How is orthogonality implemented with Miranda, Haskell, Julia, Scheme, and Erlang languages?
9
votes
0answers
211 views

NP complete problem help

I'm currently trying to find a reduction to this problem: Given a set S of n points (in the plane) in general position, is there a set of at least k triangles (formed using only points in S as ...
0
votes
0answers
31 views

Internal as well as external partition of (regular) graphs

Let $G$ be a simple finite undirected graph. Let $\{V_1,V_2\}$ be a partition of its vertex set; that is, $V_1\cup V_2=V(G)$ and $V_1\cap V_2=\emptyset$. The partition $\{V_1,V_2\}$ is said to be an ...
1
vote
0answers
51 views

Complexity class name for the class of languages that are $\Sigma^1_1$-definable over finite domains

Let ${\cal L}=\{Y_1,..., Y_k, X\}$ be a finite relational language such that $X$ is a unary relation name. Let $\phi(X,\bar{Y})\in{\cal L}$ be a first-order formula (the formula can have the equality ...
4
votes
1answer
57 views

Context weakening as an explicit rule for languages of the the lambda cube?

I'm trying to formalize the syntax and typing judgments of the Calculus of Constructions in Coq. I'm choosing to use the Pure Type Systems presentation of CoC; however, I've seen mild variations in ...
-3
votes
0answers
35 views

A variant of the Generalized Assignment problem

There are two sets $T$ and $M$. The set $T$ represents a set of tasks and the set $M$ consists of machines. A task $t_i \in T$ has two attributes: 1) a minimum-finish requirement $R_{t_i}$ and 2) an ...
-3
votes
0answers
26 views

What changes the output on this black box?

We have a theoretical black box with no obvious inputs and outputs a value. For the sake of imagination, it's a literal black box with a digital counter on one side. We want to figure out what causes ...
0
votes
0answers
32 views

Hardness of Approximation for Hypergraph Vertex Cover for Non-constant $k$

A $k$-uniform hypergraph $H = (V, E)$ consists of a set of vertices $V$ and a collection of edges $E$ of $k$-element subsets of $V$ called hyperedges. The hypergraph vertex cover problem asks for a ...
0
votes
0answers
74 views

Optimal $\ell^1$ sketching, including the coefficient

Let us define the sketch as mapping $\varphi:R^D\to R^d$, such that for arbitrary $x\in\mathbb{R}^D$, its $\ell^1$ norm is preserved up to $\epsilon$ error, with $1-\delta$ success probability: $$\...
2
votes
0answers
38 views

Energy-Based Modeling vs Deep Learning

I am doing some research on machine learning algorithms in the context of a seminar, which focuses on Energy-Based Modeling vs Deep Learning specifically in working with images Modeling. Now I know ...
-3
votes
0answers
60 views

Lower bound for SAT

It occurred to me that if a given SAT is unsatisfiable, then a DPLL algorithm must try true/false settings for all literals to determine that there does not exist any satisfying literal combination. ...
1
vote
1answer
67 views

Dynamic transitive closure with immediate new reachability facts

The typical definition of dynamic transitive closure (or reachability) uses two types of queries: the first one is an update (edge deletion/insertion) and the second one is a reachability query. Thus, ...
-1
votes
2answers
90 views

Knowing if there are two solutions to the subset sum problem

I was wondering if there are any results that say how hard it is to answer the question are there TWO subsets that sum to a fixed value? In other words, the subset sum problem but asking if there are ...
3
votes
1answer
198 views

Formalization of simulation for Turing machines

Right now I am trying to understand the concept of simulation in theoretical computer science, focussing on Universal Turing machines. All textbooks that I looked into only explain examples. They ...
-1
votes
1answer
74 views

What is the time complexity of computing intersection and union of Nondeterministic Finite Automata (NFAs)?

Assume that $\mathcal{A} = (Q_A, \Sigma, \Delta_A, q_{i_A}, F_A)$ and $\mathcal{B} = (Q_B, \Sigma, \Delta_B, q_{i_B}, F_B)$ are two NFAs. What is the worst-case time complexity of computing $\mathcal{...
7
votes
0answers
77 views

Is it possible that feedback vertex set problem has an $O(k^2/\log k)$ kernel?

(This question also suits for other similar natural $\mathrm{NP}$-hard problems) I know that there is a $4k^2$ vertex kernel (and $8k^2$ edge kernel) by Thomasse [Thomasse09] for Feedback Vertex Set (...
1
vote
0answers
196 views

Is there a known lower-bound on what the exponent could be, even if it turned out that P=NP?

Underlying motivation for the question: if someone showed that $\text{P}=\text{NP}$ but the algorithm thus produced for, e.g., $3\text{-SAT}$, runs in time $\Omega(n^G)$ where $G$ is Graham's number, ...
3
votes
0answers
61 views

Suffix array construction algorithms (SACAs)

I am working on an efficient pattern-matching algorithm (using binary files as input) based on suffix arrays. I would like to ask you If you are familiar with any suffix array construction algorithm (...
9
votes
1answer
73 views

What are the general direction and target question in the field of quantum error correction?

After quantum error correction was introduced in mid '90s, in subsequent years many of the classical analogues regarding the structure of code (such as singleton bound, GV bound etc) were obtained in ...
0
votes
1answer
101 views

When does a bipartite graph have bounded treewidth?

As the title says, I want to know when the treewidth of a bipartite graph is bounded by a constant. What families of graphs are both bipartite and bounded treewidth? More generally, I would like to ...
5
votes
2answers
207 views

Intuition behind nested positivity and counterexamples

I'm looking at the nested positivity conditions for inductive types stated in the Coq manual. First off, are there any other references (not necessarily for Coq, but in dependent type theories ...
0
votes
0answers
33 views

Online Weighted Allocations to Simulate a Distribution

I have a seemingly simple task that I want to solve using an online algorithm but unfortunately I wasn't able to find relevant resources even though it seems so basic. The inputs are $D=(d_1,\dots,d_m)...
-4
votes
0answers
51 views

Under what name is that NP-Complete commonly known? [duplicate]

When I was a student, I was explained a problem that fascinated me, and at this time, I was told it's an NP-complete problem - which I ended up reducing to a combinatory problem according to notes I ...
0
votes
0answers
29 views

what is the LP gap of this particular non metric facility location problem in planar graphs?

Suppose I have a facility location problem with all service costs 0 (or infinity (in particular service costs are not metric)) such that the edges $ij$ for which facility $i$ can service client $j$ ...
2
votes
0answers
40 views

Computational complexity problem book with solution recommendation?

I will be taking complexity class next quarter and we will use the book "B. Barak, S. Arora, Computational Complexity: A Modern Approach". However, I have little exposure to complexity ...
12
votes
2answers
278 views

Circuit and Formula Lower Bounds for Separating Sparse Sets of Strings

We say that a pair $(P,N)$ of subsets of strings from $\{0,1\}^n$ is an $n$-pair if $|P|=|N|=n$. Intuitively, sucha a pair consists of a set $P$ with $n$ positive $n$-bit strings, and a set $N$ with $...
5
votes
1answer
68 views

Survey on Quantum error correction

Are there any standard recent survey articles on quantum error correction (and may be including fault Tolerant computing)? The most standard ones that many people refer to are this and this. Both of ...
6
votes
1answer
78 views

Nonterminal descriptional complexity of regular languages

Recently I became interested in grammar complexity of regular language. Prior to searching for literature, I tried to investigate it on my own, proving two lemmas from comment below. I am aware of an ...
15
votes
2answers
915 views

Proof relevance vs. proof irrelevance

I want to use use Agda to help me write proofs, but I am getting contradictory feedback about the value of proof relevance. Jacques Carette wrote a Proof-relevant Category Theory in Agda library. But ...
12
votes
2answers
398 views

One-way randomized communication complexity of Greater-Than

Let $\mathrm{GT}_n:\{0,1\}^n \times \{0,1\}^n \to \{0,1\}$ be the greater than function: $\mathrm{GT}_n(x,y)=1$ exactly when the positive integer whose binary representation is $x$ is greater than the ...
1
vote
1answer
92 views

Why isn’t information-probability relationship linear? [closed]

I am completely new to information theory. I was learning about information content but couldn’t make sense of why the relationship between information content and probability isn’t linear? And why it ...
1
vote
0answers
28 views

Are there classes where all Eulerian orientations can be listed in polynomial time?

Is there is a subclass of regular graphs (say 4-regular graphs) for which there is a polynomial time algorithm to list all Eulerian orienations? An Eulerian orientaiton of an (undirected simple) graph ...
4
votes
1answer
96 views

Minimal clique edge cover vs minimalist (assignment-minimum) ones

Given a graph $G=(V,E)$, a clique edge cover is a collection $C$ of subsets of $V$ such that each element $c$ of $C$ is a clique ($c \times c \subseteq E$) and $G$ is the union of these cliques ($E = \...
3
votes
0answers
91 views

(Integer) Linear Program formulation of planarity?

Q: Is there an efficient (I)LP formulation of planarity? More specifically, I am looking for a set of constraints that are satisfied by exactly all planar graphs on $n$ vertices, in order to optimize ...
-2
votes
0answers
22 views

Explanation of Minimap2 Algorithm [closed]

Can someone provide a concise explanation of Minimap2 algorithm on how it is used in pairwise alignment? Here is the paper: https://academic.oup.com/bioinformatics/article/34/18/3094/4994778?login=...
2
votes
0answers
84 views

Can someone recommend a reference on graph minors structure theorem and sublinear treewidth?

Can someone recommend a reference on graph minors structure theorem and sublinear treewidth? Doesn't have to be the newest/strongest results as long as it's easier than tracking down all the papers ...
22
votes
2answers
1k views

Decidability of diophantine equations over {=, +, gcd}

It is well-known that polynomial diophantine equations are undecidable (Hilbert's 10th problem): that is, given a quantifier-free formula over the language $\{=, +, \cdot, 1\}$ (of equality, addition, ...
-3
votes
0answers
89 views

Do these examples belong to syntax or semantics and are they handled by syntactic or semantic analysis?

In the dragon book 4.3.5 Non-Context-Free Language Constructs A few syntactic constructs found in typical programming languages cannot be speci ed using grammars alone. Here, we consider two of these ...

15 30 50 per page
1
2 3 4 5
222